# Properties

 Label 303450gh Number of curves $2$ Conductor $303450$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("gh1")

sage: E.isogeny_class()

## Elliptic curves in class 303450gh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
303450.gh2 303450gh1 $$[1, 0, 0, 176862, -2313108]$$ $$2595575/1512$$ $$-356406292265625000$$ $$[]$$ $$5443200$$ $$2.0573$$ $$\Gamma_0(N)$$-optimal
303450.gh1 303450gh2 $$[1, 0, 0, -2532513, -1641484983]$$ $$-7620530425/526848$$ $$-124187792505000000000$$ $$[]$$ $$16329600$$ $$2.6066$$

## Rank

sage: E.rank()

The elliptic curves in class 303450gh have rank $$0$$.

## Complex multiplication

The elliptic curves in class 303450gh do not have complex multiplication.

## Modular form 303450.2.a.gh

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{6} + q^{7} + q^{8} + q^{9} - 6q^{11} + q^{12} + q^{13} + q^{14} + q^{16} + q^{18} - 4q^{19} + O(q^{20})$$ ## Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the Cremona numbering.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with Cremona labels. 